MATH 429 Introduction to topology
Syllabus -
Lecture notes -
Extra credit problems
- HWA-14, due 10:10, Mon. Apr. 25 (scan and upload it to CANVAS).
- Skim thru chapters 9, 12, 13, 14, 15, 16, 17, 18, and 20;
- Exercises: 12.10(e), 13.10(h), 14.6(c), 15.11(d), 18.4(a).
- Midterm in class, Fri. Apr 22, five problems:
- two problems from HWA8--HWA13;
- two theorems or its parts from the following list, possibly with related definitions:
12.4, 12.8, 12.9,
15.4, 15.12, 15.13, 15.17,
16.4, 16.5, 16.6, 16.7, 16.9, 16.10,
17.6, 17.8,
18.1,
20.1 (sketch only).
- one new problem.
-
You may prepare and use a cheat sheet --- one sided standard paper size, include diagrams and formulas, but no words. Do not make it cryptic.
- HWA-13, due 10:10, Mon. Apr. 18 (scan and upload it to CANVAS).
- Read and understand: Chapters 18 and 20;
- Read: Chapters 19;
- Exercises: 17.9(m), 18.4(f,g,k), 20.7(a).
- HWA-12, due 10:10, Mon. Apr. 11 (scan and upload it to CANVAS).
- Read and understand: Chapters 17;
- Read: Chapters 20;
- Exercises: 15.18(d), 16.11(g(i,ii,iv)), 17.9(h,p,r).
- HWA-11, due 10:10, Mon. Apr. 4 (scan and upload it to CANVAS).
- Read and understand: Chapters 15 an 16;
- Read: Chapters 17;
- Exercises: 15.11(e,g), 15.16(c), 16.11(b,f).
- HWA-10, due 10:10, Mon. Mar. 28 (scan and upload it to CANVAS).
- Read and understand: Chapters 14 an 15;
- Read: Chapters 16;
- Exercises: 14.6(e,i), 15.6(b), 15.11(a,b).
- HWA-09, due 10:10, Mon. Mar 21 (scan and upload it to CANVAS).
- Read and understand: Chapter 13;
- Exercises: 13.4(a,f), 13.10(k,n), 14.6(a).
- HWA-08, due 10:10, Mon. Mar 14 (scan and upload it to CANVAS).
- Read and understand: Chapters 9 and 12;
- Exercises: 9.8(d, e), 12.10(a,b,i) .
- Q-07, due 10:10, Fri, Mar 4 (scan and upload it to CANVAS).
- Exercises: 7.5(b), 9.8(a).
- HWA-07, due 10:10,
Mon. Feb. 28 Wed, Mar 2 (scan and upload it to CANVAS).
- Exercises: 2.9(j), 4.5(g), 5.3(d), 6.6(c), 7.13(h).
- Midterm in class,
Fri. Feb 25 Mon. Feb 28, five problems:
- two problems from HWA 01--06;
- two theorems or its parts from the following list, possibly with related definitions:
2.5, 2.7,
3.3, 3.5,
4.4,
5.2, 5.8, 5.12,
6.3, 6.5,
7.7, 7.8, 7.10, 7.11(only-if part),
8.5, 8.7, 8.8, 8.10,
9.6, 9.7.
- one new problem.
- You may prepare and use a cheat sheet --- one sided standard paper size, include diagrams and formulas, but no words. Do not make it cryptic.
- HWA-06, due 10:10, Mon. Feb. 21 (scan and upload it to CANVAS).
- Read and understand: Chapters 8 and 9;
- Skim thru chapters 1--9; prepare questions.
- Exercises: 8.14(a,f,i), 9.8(e,f).
- HWA-05, due 10:10, Mon. Feb. 14 (scan and upload it to CANVAS).
- Read and understand: Chapter 7;
- Read: Chapter 8;
- Exercises: 6.6(l), 7.5(c), 7.13(b, c), 8.14(b).
- HWA-04, due 10:10, Mon. Feb 7 (scan and upload it to CANVAS).
- Read and understand: Chapter 6 and Lecture 6;
- Read: Chapter 7;
- Exercises: 3.7(d), 5.3(g), 6.2(d), 7.5(a), and the following:
Let \(\mathscr{B}\) be a base for the topology on \(Y\).
Show that a map \(f\colon X \to Y\) is continuous if and only if \(f^{-1}(B)\) is open for any set \(B\in\mathscr{B}\).
Prove the same assuming that \(\mathscr{B}\) is a prebase.
- HWA-03, due 10:10, Mon. Jan. 31 (scan and upload it to CANVAS).
- Read and understand: Chapter 4 and 5;
- Read: Chapter 0 and 6;
- Exercises: 4.5(e), 5.3(b), 5.9(c), 5.13(b), 6.2(c).
- HWA-02, due 10:10, Mon. Jan. 24 (scan and upload it to CANVAS).
- Read and understand: Chapter 2 and 3;
- Read: Chapter 4;
- Exercises: 2.6(d), 2.8(b), 2.9(d), 3.7(a), 4.5(d).
- HWA-01, due 10:10, Fri, Jan. 14 (scan and upload it to CANVAS).
- Read and understand: Chapter 1;
- Read: Chapter 2;
- Exercises: 1.5(a, b), 1.8(a, d), 2.3(c).